// Copyright 2011 Google Inc. All Rights Reserved.

//

// Use of this source code is governed by a BSD-style license

// that can be found in the COPYING file in the root of the source

// tree. An additional intellectual property rights grant can be found

// in the file PATENTS. All contributing project authors may

// be found in the AUTHORS file in the root of the source tree.

// -----------------------------------------------------------------------------

//

//   Quantization

//

// Author: Skal (pascal.massimino@gmail.com)

#include <assert.h>

#include <math.h>

#include <stdlib.h>  // for abs()

#include <string.h>

#include "src/dec/common_dec.h"

#include "src/dsp/dsp.h"

#include "src/dsp/quant.h"

#include "src/enc/cost_enc.h"

#include "src/enc/vp8i_enc.h"

#include "src/webp/types.h"

#define DO_TRELLIS_I4  1

#define DO_TRELLIS_I16 1   // not a huge gain, but ok at low bitrate.

#define DO_TRELLIS_UV  0   // disable trellis for UV. Risky. Not worth.

#define USE_TDISTO 1

#define MID_ALPHA 64      // neutral value for susceptibility

#define MIN_ALPHA 30      // lowest usable value for susceptibility

#define MAX_ALPHA 100     // higher meaningful value for susceptibility

#define SNS_TO_DQ 0.9     // Scaling constant between the sns value and the QP

                          // power-law modulation. Must be strictly less than 1.

// number of non-zero coeffs below which we consider the block very flat

// (and apply a penalty to complex predictions)

#define FLATNESS_LIMIT_I16 0       // I16 mode (special case)

#define FLATNESS_LIMIT_I4  3       // I4 mode

#define FLATNESS_LIMIT_UV  2       // UV mode

#define FLATNESS_PENALTY   140     // roughly ~1bit per block

#define MULT_8B(a, b) (((a) * (b) + 128) >> 8)

#define RD_DISTO_MULT      256  // distortion multiplier (equivalent of lambda)

// #define DEBUG_BLOCK

//------------------------------------------------------------------------------

#if defined(DEBUG_BLOCK)

#include <stdio.h>

#include <stdlib.h>

static void PrintBlockInfo(const VP8EncIterator* const it,

                           const VP8ModeScore* const rd) {

  int i, j;

  const int is_i16 = (it->mb->type == 1);

  const uint8_t* const y_in = it->yuv_in + Y_OFF_ENC;

  const uint8_t* const y_out = it->yuv_out + Y_OFF_ENC;

  const uint8_t* const uv_in = it->yuv_in + U_OFF_ENC;

  const uint8_t* const uv_out = it->yuv_out + U_OFF_ENC;

  printf("SOURCE / OUTPUT / ABS DELTA\n");

  for (j = 0; j < 16; ++j) {

    for (i = 0; i < 16; ++i) printf("%3d ", y_in[i + j * BPS]);

    printf("     ");

    for (i = 0; i < 16; ++i) printf("%3d ", y_out[i + j * BPS]);

    printf("     ");

    for (i = 0; i < 16; ++i) {

      printf("%1d ", abs(y_in[i + j * BPS] - y_out[i + j * BPS]));

    }

    printf("\n");

  }

  printf("\n");   // newline before the U/V block

  for (j = 0; j < 8; ++j) {

    for (i = 0; i < 8; ++i) printf("%3d ", uv_in[i + j * BPS]);

    printf(" ");

    for (i = 8; i < 16; ++i) printf("%3d ", uv_in[i + j * BPS]);

    printf("    ");

    for (i = 0; i < 8; ++i) printf("%3d ", uv_out[i + j * BPS]);

    printf(" ");

    for (i = 8; i < 16; ++i) printf("%3d ", uv_out[i + j * BPS]);

    printf("   ");

    for (i = 0; i < 8; ++i) {

      printf("%1d ", abs(uv_out[i + j * BPS] - uv_in[i + j * BPS]));

    }

    printf(" ");

    for (i = 8; i < 16; ++i) {

      printf("%1d ", abs(uv_out[i + j * BPS] - uv_in[i + j * BPS]));

    }

    printf("\n");

  }

  printf("\nD:%d SD:%d R:%d H:%d nz:0x%x score:%d\n",

    (int)rd->D, (int)rd->SD, (int)rd->R, (int)rd->H, (int)rd->nz,

    (int)rd->score);

  if (is_i16) {

    printf("Mode: %d\n", rd->mode_i16);

    printf("y_dc_levels:");

    for (i = 0; i < 16; ++i) printf("%3d ", rd->y_dc_levels[i]);

    printf("\n");

  } else {

    printf("Modes[16]: ");

    for (i = 0; i < 16; ++i) printf("%d ", rd->modes_i4[i]);

    printf("\n");

  }

  printf("y_ac_levels:\n");

  for (j = 0; j < 16; ++j) {

    for (i = is_i16 ? 1 : 0; i < 16; ++i) {

      printf("%4d ", rd->y_ac_levels[j][i]);

    }

    printf("\n");

  }

  printf("\n");

  printf("uv_levels (mode=%d):\n", rd->mode_uv);

  for (j = 0; j < 8; ++j) {

    for (i = 0; i < 16; ++i) {

      printf("%4d ", rd->uv_levels[j][i]);

    }

    printf("\n");

  }

}

#endif   // DEBUG_BLOCK

//------------------------------------------------------------------------------

static WEBP_INLINE int clip(int v, int m, int M) {

  return v < m ? m : v > M ? M : v;

}

static const uint8_t kZigzag[16] = {

  0, 1, 4, 8, 5, 2, 3, 6, 9, 12, 13, 10, 7, 11, 14, 15

};

static const uint8_t kDcTable[128] = {

  4,     5,   6,   7,   8,   9,  10,  10,

  11,   12,  13,  14,  15,  16,  17,  17,

  18,   19,  20,  20,  21,  21,  22,  22,

  23,   23,  24,  25,  25,  26,  27,  28,

  29,   30,  31,  32,  33,  34,  35,  36,

  37,   37,  38,  39,  40,  41,  42,  43,

  44,   45,  46,  46,  47,  48,  49,  50,

  51,   52,  53,  54,  55,  56,  57,  58,

  59,   60,  61,  62,  63,  64,  65,  66,

  67,   68,  69,  70,  71,  72,  73,  74,

  75,   76,  76,  77,  78,  79,  80,  81,

  82,   83,  84,  85,  86,  87,  88,  89,

  91,   93,  95,  96,  98, 100, 101, 102,

  104, 106, 108, 110, 112, 114, 116, 118,

  122, 124, 126, 128, 130, 132, 134, 136,

  138, 140, 143, 145, 148, 151, 154, 157

};

static const uint16_t kAcTable[128] = {

  4,     5,   6,   7,   8,   9,  10,  11,

  12,   13,  14,  15,  16,  17,  18,  19,

  20,   21,  22,  23,  24,  25,  26,  27,

  28,   29,  30,  31,  32,  33,  34,  35,

  36,   37,  38,  39,  40,  41,  42,  43,

  44,   45,  46,  47,  48,  49,  50,  51,

  52,   53,  54,  55,  56,  57,  58,  60,

  62,   64,  66,  68,  70,  72,  74,  76,

  78,   80,  82,  84,  86,  88,  90,  92,

  94,   96,  98, 100, 102, 104, 106, 108,

  110, 112, 114, 116, 119, 122, 125, 128,

  131, 134, 137, 140, 143, 146, 149, 152,

  155, 158, 161, 164, 167, 170, 173, 177,

  181, 185, 189, 193, 197, 201, 205, 209,

  213, 217, 221, 225, 229, 234, 239, 245,

  249, 254, 259, 264, 269, 274, 279, 284

};

static const uint16_t kAcTable2[128] = {

  8,     8,   9,  10,  12,  13,  15,  17,

  18,   20,  21,  23,  24,  26,  27,  29,

  31,   32,  34,  35,  37,  38,  40,  41,

  43,   44,  46,  48,  49,  51,  52,  54,

  55,   57,  58,  60,  62,  63,  65,  66,

  68,   69,  71,  72,  74,  75,  77,  79,

  80,   82,  83,  85,  86,  88,  89,  93,

  96,   99, 102, 105, 108, 111, 114, 117,

  120, 124, 127, 130, 133, 136, 139, 142,

  145, 148, 151, 155, 158, 161, 164, 167,

  170, 173, 176, 179, 184, 189, 193, 198,

  203, 207, 212, 217, 221, 226, 230, 235,

  240, 244, 249, 254, 258, 263, 268, 274,

  280, 286, 292, 299, 305, 311, 317, 323,

  330, 336, 342, 348, 354, 362, 370, 379,

  385, 393, 401, 409, 416, 424, 432, 440

};

static const uint8_t kBiasMatrices[3][2] = {  // [luma-ac,luma-dc,chroma][dc,ac]

  { 96, 110 }, { 96, 108 }, { 110, 115 }

};

// Sharpening by (slightly) raising the hi-frequency coeffs.

// Hack-ish but helpful for mid-bitrate range. Use with care.

#define SHARPEN_BITS 11  // number of descaling bits for sharpening bias

static const uint8_t kFreqSharpening[16] = {

  0,  30, 60, 90,

  30, 60, 90, 90,

  60, 90, 90, 90,

  90, 90, 90, 90

};

//------------------------------------------------------------------------------

// Initialize quantization parameters in VP8Matrix

// Returns the average quantizer

static int ExpandMatrix(VP8Matrix* const m, int type) {

  int i, sum;

  for (i = 0; i < 2; ++i) {

    const int is_ac_coeff = (i > 0);

    const int bias = kBiasMatrices[type][is_ac_coeff];

    m->iq[i] = (1 << QFIX) / m->q[i];

    m->bias[i] = BIAS(bias);

    // zthresh is the exact value such that QUANTDIV(coeff, iQ, B) is:

    //   * zero if coeff <= zthresh

    //   * non-zero if coeff > zthresh

    m->zthresh[i] = ((1 << QFIX) - 1 - m->bias[i]) / m->iq[i];

  }

  for (i = 2; i < 16; ++i) {

    m->q[i] = m->q[1];

    m->iq[i] = m->iq[1];

    m->bias[i] = m->bias[1];

    m->zthresh[i] = m->zthresh[1];

  }

  for (sum = 0, i = 0; i < 16; ++i) {

    if (type == 0) {  // we only use sharpening for AC luma coeffs

      m->sharpen[i] = (kFreqSharpening[i] * m->q[i]) >> SHARPEN_BITS;

    } else {

      m->sharpen[i] = 0;

    }

    sum += m->q[i];

  }

  return (sum + 8) >> 4;

}

static void CheckLambdaValue(int* const v) { if (*v < 1) *v = 1; }

static void SetupMatrices(VP8Encoder* enc) {

  int i;

  const int tlambda_scale =

    (enc->method >= 4) ? enc->config->sns_strength

                        : 0;

  const int num_segments = enc->segment_hdr.num_segments;

  for (i = 0; i < num_segments; ++i) {

    VP8SegmentInfo* const m = &enc->dqm[i];

    const int q = m->quant;

    int q_i4, q_i16, q_uv;

    m->y1.q[0] = kDcTable[clip(q + enc->dq_y1_dc, 0, 127)];

    m->y1.q[1] = kAcTable[clip(q,                  0, 127)];

    m->y2.q[0] = kDcTable[ clip(q + enc->dq_y2_dc, 0, 127)] * 2;

    m->y2.q[1] = kAcTable2[clip(q + enc->dq_y2_ac, 0, 127)];

    m->uv.q[0] = kDcTable[clip(q + enc->dq_uv_dc, 0, 117)];

    m->uv.q[1] = kAcTable[clip(q + enc->dq_uv_ac, 0, 127)];

    q_i4  = ExpandMatrix(&m->y1, 0);

    q_i16 = ExpandMatrix(&m->y2, 1);

    q_uv  = ExpandMatrix(&m->uv, 2);

    m->lambda_i4          = (3 * q_i4 * q_i4) >> 7;

    m->lambda_i16         = (3 * q_i16 * q_i16);

    m->lambda_uv          = (3 * q_uv * q_uv) >> 6;

    m->lambda_mode        = (1 * q_i4 * q_i4) >> 7;

    m->lambda_trellis_i4  = (7 * q_i4 * q_i4) >> 3;

    m->lambda_trellis_i16 = (q_i16 * q_i16) >> 2;

    m->lambda_trellis_uv  = (q_uv * q_uv) << 1;

    m->tlambda            = (tlambda_scale * q_i4) >> 5;

    // none of these constants should be < 1

    CheckLambdaValue(&m->lambda_i4);

    CheckLambdaValue(&m->lambda_i16);

    CheckLambdaValue(&m->lambda_uv);

    CheckLambdaValue(&m->lambda_mode);

    CheckLambdaValue(&m->lambda_trellis_i4);

    CheckLambdaValue(&m->lambda_trellis_i16);

    CheckLambdaValue(&m->lambda_trellis_uv);

    CheckLambdaValue(&m->tlambda);

    m->min_disto = 20 * m->y1.q[0];   // quantization-aware min disto

    m->max_edge  = 0;

    m->i4_penalty = 1000 * q_i4 * q_i4;

  }

}

//------------------------------------------------------------------------------

// Initialize filtering parameters

// Very small filter-strength values have close to no visual effect. So we can

// save a little decoding-CPU by turning filtering off for these.

#define FSTRENGTH_CUTOFF 2

static void SetupFilterStrength(VP8Encoder* const enc) {

  int i;

  // level0 is in [0..500]. Using '-f 50' as filter_strength is mid-filtering.

  const int level0 = 5 * enc->config->filter_strength;

  for (i = 0; i < NUM_MB_SEGMENTS; ++i) {

    VP8SegmentInfo* const m = &enc->dqm[i];

    // We focus on the quantization of AC coeffs.

    const int qstep = kAcTable[clip(m->quant, 0, 127)] >> 2;

    const int base_strength =

        VP8FilterStrengthFromDelta(enc->filter_hdr.sharpness, qstep);

    // Segments with lower complexity ('beta') will be less filtered.

    const int f = base_strength * level0 / (256 + m->beta);

    m->fstrength = (f < FSTRENGTH_CUTOFF) ? 0 : (f > 63) ? 63 : f;

  }

  // We record the initial strength (mainly for the case of 1-segment only).

  enc->filter_hdr.level = enc->dqm[0].fstrength;

  enc->filter_hdr.simple = (enc->config->filter_type == 0);

  enc->filter_hdr.sharpness = enc->config->filter_sharpness;

}

//------------------------------------------------------------------------------

// Note: if you change the values below, remember that the max range

// allowed by the syntax for DQ_UV is [-16,16].

#define MAX_DQ_UV (6)

#define MIN_DQ_UV (-4)

// We want to emulate jpeg-like behaviour where the expected "good" quality

// is around q=75. Internally, our "good" middle is around c=50. So we

// map accordingly using linear piece-wise function

static double QualityToCompression(double c) {

  const double linear_c = (c < 0.75) ? c * (2. / 3.) : 2. * c - 1.;

  // The file size roughly scales as pow(quantizer, 3.). Actually, the

  // exponent is somewhere between 2.8 and 3.2, but we're mostly interested

  // in the mid-quant range. So we scale the compressibility inversely to

  // this power-law: quant ~= compression ^ 1/3. This law holds well for

  // low quant. Finer modeling for high-quant would make use of kAcTable[]

  // more explicitly.

  const double v = pow(linear_c, 1 / 3.);

  return v;

}

static double QualityToJPEGCompression(double c, double alpha) {

  // We map the complexity 'alpha' and quality setting 'c' to a compression

  // exponent empirically matched to the compression curve of libjpeg6b.

  // On average, the WebP output size will be roughly similar to that of a

  // JPEG file compressed with same quality factor.

  const double amin = 0.30;

  const double amax = 0.85;

  const double exp_min = 0.4;

  const double exp_max = 0.9;

  const double slope = (exp_min - exp_max) / (amax - amin);

  // Linearly interpolate 'expn' from exp_min to exp_max

  // in the [amin, amax] range.

  const double expn = (alpha > amax) ? exp_min

                    : (alpha < amin) ? exp_max

                    : exp_max + slope * (alpha - amin);

  const double v = pow(c, expn);

  return v;

}

static int SegmentsAreEquivalent(const VP8SegmentInfo* const S1,

                                 const VP8SegmentInfo* const S2) {

  return (S1->quant == S2->quant) && (S1->fstrength == S2->fstrength);

}

static void SimplifySegments(VP8Encoder* const enc) {

  int map[NUM_MB_SEGMENTS] = { 0, 1, 2, 3 };

  // 'num_segments' is previously validated and <= NUM_MB_SEGMENTS, but an

  // explicit check is needed to avoid a spurious warning about 'i' exceeding

  // array bounds of 'dqm' with some compilers (noticed with gcc-4.9).

  const int num_segments = (enc->segment_hdr.num_segments < NUM_MB_SEGMENTS)

                               ? enc->segment_hdr.num_segments

                               : NUM_MB_SEGMENTS;

  int num_final_segments = 1;

  int s1, s2;

  for (s1 = 1; s1 < num_segments; ++s1) {    // find similar segments

    const VP8SegmentInfo* const S1 = &enc->dqm[s1];

    int found = 0;

    // check if we already have similar segment

    for (s2 = 0; s2 < num_final_segments; ++s2) {

      const VP8SegmentInfo* const S2 = &enc->dqm[s2];

      if (SegmentsAreEquivalent(S1, S2)) {

        found = 1;

        break;

      }

    }

    map[s1] = s2;

    if (!found) {

      if (num_final_segments != s1) {

        enc->dqm[num_final_segments] = enc->dqm[s1];

      }

      ++num_final_segments;

    }

  }

  if (num_final_segments < num_segments) {  // Remap

    int i = enc->mb_w * enc->mb_h;

    while (i-- > 0) enc->mb_info[i].segment = map[enc->mb_info[i].segment];

    enc->segment_hdr.num_segments = num_final_segments;

    // Replicate the trailing segment infos (it's mostly cosmetics)

    for (i = num_final_segments; i < num_segments; ++i) {

      enc->dqm[i] = enc->dqm[num_final_segments - 1];

    }

  }

}

void VP8SetSegmentParams(VP8Encoder* const enc, float quality) {

  int i;

  int dq_uv_ac, dq_uv_dc;

  const int num_segments = enc->segment_hdr.num_segments;

  const double amp = SNS_TO_DQ * enc->config->sns_strength / 100. / 128.;

  const double Q = quality / 100.;

  const double c_base = enc->config->emulate_jpeg_size ?

      QualityToJPEGCompression(Q, enc->alpha / 255.) :

      QualityToCompression(Q);

  for (i = 0; i < num_segments; ++i) {

    // We modulate the base coefficient to accommodate for the quantization

    // susceptibility and allow denser segments to be quantized more.

    const double expn = 1. - amp * enc->dqm[i].alpha;

    const double c = pow(c_base, expn);

    const int q = (int)(127. * (1. - c));

    assert(expn > 0.);

    enc->dqm[i].quant = clip(q, 0, 127);

  }

  // purely indicative in the bitstream (except for the 1-segment case)

  enc->base_quant = enc->dqm[0].quant;

  // fill-in values for the unused segments (required by the syntax)

  for (i = num_segments; i < NUM_MB_SEGMENTS; ++i) {

    enc->dqm[i].quant = enc->base_quant;

  }

  // uv_alpha is normally spread around ~60. The useful range is

  // typically ~30 (quite bad) to ~100 (ok to decimate UV more).

  // We map it to the safe maximal range of MAX/MIN_DQ_UV for dq_uv.

  dq_uv_ac = (enc->uv_alpha - MID_ALPHA) * (MAX_DQ_UV - MIN_DQ_UV)

                                         / (MAX_ALPHA - MIN_ALPHA);

  // we rescale by the user-defined strength of adaptation

  dq_uv_ac = dq_uv_ac * enc->config->sns_strength / 100;

  // and make it safe.

  dq_uv_ac = clip(dq_uv_ac, MIN_DQ_UV, MAX_DQ_UV);

  // We also boost the dc-uv-quant a little, based on sns-strength, since

  // U/V channels are quite more reactive to high quants (flat DC-blocks

  // tend to appear, and are unpleasant).

  dq_uv_dc = -4 * enc->config->sns_strength / 100;

  dq_uv_dc = clip(dq_uv_dc, -15, 15);   // 4bit-signed max allowed

  enc->dq_y1_dc = 0;       // TODO(skal): dq-lum

  enc->dq_y2_dc = 0;

  enc->dq_y2_ac = 0;

  enc->dq_uv_dc = dq_uv_dc;

  enc->dq_uv_ac = dq_uv_ac;

  SetupFilterStrength(enc);   // initialize segments' filtering, eventually

  if (num_segments > 1) SimplifySegments(enc);

  SetupMatrices(enc);         // finalize quantization matrices

}

//------------------------------------------------------------------------------

// Form the predictions in cache

// Must be ordered using {DC_PRED, TM_PRED, V_PRED, H_PRED} as index

const uint16_t VP8I16ModeOffsets[4] = { I16DC16, I16TM16, I16VE16, I16HE16 };

const uint16_t VP8UVModeOffsets[4] = { C8DC8, C8TM8, C8VE8, C8HE8 };

// Must be indexed using {B_DC_PRED -> B_HU_PRED} as index

static const uint16_t VP8I4ModeOffsets[NUM_BMODES] = {

  I4DC4, I4TM4, I4VE4, I4HE4, I4RD4, I4VR4, I4LD4, I4VL4, I4HD4, I4HU4

};

void VP8MakeLuma16Preds(const VP8EncIterator* const it) {

  const uint8_t* const left = it->x ? it->y_left : NULL;

  const uint8_t* const top = it->y ? it->y_top : NULL;

  VP8EncPredLuma16(it->yuv_p, left, top);

}

void VP8MakeChroma8Preds(const VP8EncIterator* const it) {

  const uint8_t* const left = it->x ? it->u_left : NULL;

  const uint8_t* const top = it->y ? it->uv_top : NULL;

  VP8EncPredChroma8(it->yuv_p, left, top);

}

// Form all the ten Intra4x4 predictions in the 'yuv_p' cache

// for the 4x4 block it->i4

static void MakeIntra4Preds(const VP8EncIterator* const it) {

  VP8EncPredLuma4(it->yuv_p, it->i4_top);

}

//------------------------------------------------------------------------------

// Quantize

// Layout:

// +----+----+

// |YYYY|UUVV| 0

// |YYYY|UUVV| 4

// |YYYY|....| 8

// |YYYY|....| 12

// +----+----+

const uint16_t VP8Scan[16] = {  // Luma

  0 +  0 * BPS,  4 +  0 * BPS, 8 +  0 * BPS, 12 +  0 * BPS,

  0 +  4 * BPS,  4 +  4 * BPS, 8 +  4 * BPS, 12 +  4 * BPS,

  0 +  8 * BPS,  4 +  8 * BPS, 8 +  8 * BPS, 12 +  8 * BPS,

  0 + 12 * BPS,  4 + 12 * BPS, 8 + 12 * BPS, 12 + 12 * BPS,

};

static const uint16_t VP8ScanUV[4 + 4] = {

  0 + 0 * BPS,   4 + 0 * BPS, 0 + 4 * BPS,  4 + 4 * BPS,    // U

  8 + 0 * BPS,  12 + 0 * BPS, 8 + 4 * BPS, 12 + 4 * BPS     // V

};

//------------------------------------------------------------------------------

// Distortion measurement

static const uint16_t kWeightY[16] = {

  38, 32, 20, 9, 32, 28, 17, 7, 20, 17, 10, 4, 9, 7, 4, 2

};

static const uint16_t kWeightTrellis[16] = {

#if USE_TDISTO == 0

  16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

#else

  30, 27, 19, 11,

  27, 24, 17, 10,

  19, 17, 12,  8,

  11, 10,  8,  6

#endif

};

// Init/Copy the common fields in score.

static void InitScore(VP8ModeScore* const rd) {

  rd->D  = 0;

  rd->SD = 0;

  rd->R  = 0;

  rd->H  = 0;

  rd->nz = 0;

  rd->score = MAX_COST;

}

static void CopyScore(VP8ModeScore* WEBP_RESTRICT const dst,

                      const VP8ModeScore* WEBP_RESTRICT const src) {

  dst->D  = src->D;

  dst->SD = src->SD;

  dst->R  = src->R;

  dst->H  = src->H;

  dst->nz = src->nz;      // note that nz is not accumulated, but just copied.

  dst->score = src->score;

}

static void AddScore(VP8ModeScore* WEBP_RESTRICT const dst,

                     const VP8ModeScore* WEBP_RESTRICT const src) {

  dst->D  += src->D;

  dst->SD += src->SD;

  dst->R  += src->R;

  dst->H  += src->H;

  dst->nz |= src->nz;     // here, new nz bits are accumulated.

  dst->score += src->score;

}

//------------------------------------------------------------------------------

// Performs trellis-optimized quantization.

// Trellis node

typedef struct {

  int8_t prev;            // best previous node

  int8_t sign;            // sign of coeff_i

  int16_t level;          // level

} Node;

// Score state

typedef struct {

  score_t score;          // partial RD score

  const uint16_t* costs;  // shortcut to cost tables

} ScoreState;

// If a coefficient was quantized to a value Q (using a neutral bias),

// we test all alternate possibilities between [Q-MIN_DELTA, Q+MAX_DELTA]

// We don't test negative values though.

#define MIN_DELTA 0   // how much lower level to try

#define MAX_DELTA 1   // how much higher

#define NUM_NODES (MIN_DELTA + 1 + MAX_DELTA)

#define NODE(n, l) (nodes[(n)][(l) + MIN_DELTA])

#define SCORE_STATE(n, l) (score_states[n][(l) + MIN_DELTA])

static WEBP_INLINE void SetRDScore(int lambda, VP8ModeScore* const rd) {

  rd->score = (rd->R + rd->H) * lambda + RD_DISTO_MULT * (rd->D + rd->SD);

}

static WEBP_INLINE score_t RDScoreTrellis(int lambda, score_t rate,

                                          score_t distortion) {

  return rate * lambda + RD_DISTO_MULT * distortion;

}

// Coefficient type.

enum { TYPE_I16_AC = 0, TYPE_I16_DC = 1, TYPE_CHROMA_A = 2, TYPE_I4_AC = 3 };

static int TrellisQuantizeBlock(const VP8Encoder* WEBP_RESTRICT const enc,

                                int16_t in[16], int16_t out[16],

                                int ctx0, int coeff_type,

                                const VP8Matrix* WEBP_RESTRICT const mtx,

                                int lambda) {

  const ProbaArray* const probas = enc->proba.coeffs[coeff_type];

  CostArrayPtr const costs =

      (CostArrayPtr)enc->proba.remapped_costs[coeff_type];

  const int first = (coeff_type == TYPE_I16_AC) ? 1 : 0;

  Node nodes[16][NUM_NODES];

  ScoreState score_states[2][NUM_NODES];

  ScoreState* ss_cur = &SCORE_STATE(0, MIN_DELTA);

  ScoreState* ss_prev = &SCORE_STATE(1, MIN_DELTA);

  int best_path[3] = {-1, -1, -1};   // store best-last/best-level/best-previous

  score_t best_score;

  int n, m, p, last;

  {

    score_t cost;

    const int thresh = mtx->q[1] * mtx->q[1] / 4;

    const int last_proba = probas[VP8EncBands[first]][ctx0][0];

    // compute the position of the last interesting coefficient

    last = first - 1;

    for (n = 15; n >= first; --n) {

      const int j = kZigzag[n];

      const int err = in[j] * in[j];

      if (err > thresh) {

        last = n;

        break;

      }

    }

    // we don't need to go inspect up to n = 16 coeffs. We can just go up

    // to last + 1 (inclusive) without losing much.

    if (last < 15) ++last;

    // compute 'skip' score. This is the max score one can do.

    cost = VP8BitCost(0, last_proba);

    best_score = RDScoreTrellis(lambda, cost, 0);

    // initialize source node.

    for (m = -MIN_DELTA; m <= MAX_DELTA; ++m) {

      const score_t rate = (ctx0 == 0) ? VP8BitCost(1, last_proba) : 0;

      ss_cur[m].score = RDScoreTrellis(lambda, rate, 0);

      ss_cur[m].costs = costs[first][ctx0];

    }

  }

  // traverse trellis.

  for (n = first; n <= last; ++n) {

    const int j = kZigzag[n];

    const uint32_t Q  = mtx->q[j];

    const uint32_t iQ = mtx->iq[j];

    const uint32_t B = BIAS(0x00);     // neutral bias

    // note: it's important to take sign of the _original_ coeff,

    // so we don't have to consider level < 0 afterward.

    const int sign = (in[j] < 0);

    const uint32_t coeff0 = (sign ? -in[j] : in[j]) + mtx->sharpen[j];

    int level0 = QUANTDIV(coeff0, iQ, B);

    int thresh_level = QUANTDIV(coeff0, iQ, BIAS(0x80));

    if (thresh_level > MAX_LEVEL) thresh_level = MAX_LEVEL;

    if (level0 > MAX_LEVEL) level0 = MAX_LEVEL;

    {   // Swap current and previous score states

      ScoreState* const tmp = ss_cur;

      ss_cur = ss_prev;

      ss_prev = tmp;

    }

    // test all alternate level values around level0.

    for (m = -MIN_DELTA; m <= MAX_DELTA; ++m) {

      Node* const cur = &NODE(n, m);

      const int level = level0 + m;

      const int ctx = (level > 2) ? 2 : level;

      const int band = VP8EncBands[n + 1];

      score_t base_score;

      score_t best_cur_score;

      int best_prev;

      score_t cost, score;

      ss_cur[m].costs = costs[n + 1][ctx];

      if (level < 0 || level > thresh_level) {

        ss_cur[m].score = MAX_COST;

        // Node is dead.

        continue;

      }

      {

        // Compute delta_error = how much coding this level will

        // subtract to max_error as distortion.

        // Here, distortion = sum of (|coeff_i| - level_i * Q_i)^2

        const int new_error = coeff0 - level * Q;

        const int delta_error =

            kWeightTrellis[j] * (new_error * new_error - coeff0 * coeff0);

        base_score = RDScoreTrellis(lambda, 0, delta_error);

      }

      // Inspect all possible non-dead predecessors. Retain only the best one.

      // The base_score is added to all scores so it is only added for the final

      // value after the loop.

      cost = VP8LevelCost(ss_prev[-MIN_DELTA].costs, level);

      best_cur_score =

          ss_prev[-MIN_DELTA].score + RDScoreTrellis(lambda, cost, 0);

      best_prev = -MIN_DELTA;

      for (p = -MIN_DELTA + 1; p <= MAX_DELTA; ++p) {

        // Dead nodes (with ss_prev[p].score >= MAX_COST) are automatically

        // eliminated since their score can't be better than the current best.

        cost = VP8LevelCost(ss_prev[p].costs, level);

        // Examine node assuming it's a non-terminal one.

        score = ss_prev[p].score + RDScoreTrellis(lambda, cost, 0);

        if (score < best_cur_score) {

          best_cur_score = score;

          best_prev = p;

        }

      }

      best_cur_score += base_score;

      // Store best finding in current node.

      cur->sign = sign;

      cur->level = level;

      cur->prev = best_prev;

      ss_cur[m].score = best_cur_score;

      // Now, record best terminal node (and thus best entry in the graph).

      if (level != 0 && best_cur_score < best_score) {

        const score_t last_pos_cost =

            (n < 15) ? VP8BitCost(0, probas[band][ctx][0]) : 0;

        const score_t last_pos_score = RDScoreTrellis(lambda, last_pos_cost, 0);

        score = best_cur_score + last_pos_score;

        if (score < best_score) {

          best_score = score;

          best_path[0] = n;                     // best eob position

          best_path[1] = m;                     // best node index

          best_path[2] = best_prev;             // best predecessor

        }

      }

    }

  }

  // Fresh start

  // Beware! We must preserve in[0]/out[0] value for TYPE_I16_AC case.

  if (coeff_type == TYPE_I16_AC) {

    memset(in + 1, 0, 15 * sizeof(*in));

    memset(out + 1, 0, 15 * sizeof(*out));

  } else {

    memset(in, 0, 16 * sizeof(*in));

    memset(out, 0, 16 * sizeof(*out));

  }

  if (best_path[0] == -1) {

    return 0;  // skip!

  }

  {

    // Unwind the best path.

    // Note: best-prev on terminal node is not necessarily equal to the

    // best_prev for non-terminal. So we patch best_path[2] in.

    int nz = 0;

    int best_node = best_path[1];

    n = best_path[0];

    NODE(n, best_node).prev = best_path[2];   // force best-prev for terminal

    for (; n >= first; --n) {

      const Node* const node = &NODE(n, best_node);

      const int j = kZigzag[n];

      out[n] = node->sign ? -node->level : node->level;

      nz |= node->level;

      in[j] = out[n] * mtx->q[j];

      best_node = node->prev;

    }

    return (nz != 0);

  }

}

#undef NODE

//------------------------------------------------------------------------------

// Performs: difference, transform, quantize, back-transform, add

// all at once. Output is the reconstructed block in *yuv_out, and the

// quantized levels in *levels.

static int ReconstructIntra16(VP8EncIterator* WEBP_RESTRICT const it,

                              VP8ModeScore* WEBP_RESTRICT const rd,

                              uint8_t* WEBP_RESTRICT const yuv_out,

                              int mode) {

  const VP8Encoder* const enc = it->enc;

  const uint8_t* const ref = it->yuv_p + VP8I16ModeOffsets[mode];

  const uint8_t* const src = it->yuv_in + Y_OFF_ENC;

  const VP8SegmentInfo* const dqm = &enc->dqm[it->mb->segment];

  int nz = 0;

  int n;

  int16_t tmp[16][16], dc_tmp[16];

  for (n = 0; n < 16; n += 2) {

    VP8FTransform2(src + VP8Scan[n], ref + VP8Scan[n], tmp[n]);

  }

  VP8FTransformWHT(tmp[0], dc_tmp);

  nz |= VP8EncQuantizeBlockWHT(dc_tmp, rd->y_dc_levels, &dqm->y2) << 24;

  if (DO_TRELLIS_I16 && it->do_trellis) {

    int x, y;

    VP8IteratorNzToBytes(it);

    for (y = 0, n = 0; y < 4; ++y) {

      for (x = 0; x < 4; ++x, ++n) {

        const int ctx = it->top_nz[x] + it->left_nz[y];

        const int non_zero = TrellisQuantizeBlock(

            enc, tmp[n], rd->y_ac_levels[n], ctx, TYPE_I16_AC, &dqm->y1,

            dqm->lambda_trellis_i16);

        it->top_nz[x] = it->left_nz[y] = non_zero;

        rd->y_ac_levels[n][0] = 0;

        nz |= non_zero << n;

      }

    }

  } else {

    for (n = 0; n < 16; n += 2) {

      // Zero-out the first coeff, so that: a) nz is correct below, and

      // b) finding 'last' non-zero coeffs in SetResidualCoeffs() is simplified.

      tmp[n][0] = tmp[n + 1][0] = 0;

      nz |= VP8EncQuantize2Blocks(tmp[n], rd->y_ac_levels[n], &dqm->y1) << n;

      assert(rd->y_ac_levels[n + 0][0] == 0);

      assert(rd->y_ac_levels[n + 1][0] == 0);

    }

  }

  // Transform back

  VP8TransformWHT(dc_tmp, tmp[0]);

  for (n = 0; n < 16; n += 2) {

    VP8ITransform(ref + VP8Scan[n], tmp[n], yuv_out + VP8Scan[n], 1);

  }

  return nz;

}

static int ReconstructIntra4(VP8EncIterator* WEBP_RESTRICT const it,

                             int16_t levels[16],

                             const uint8_t* WEBP_RESTRICT const src,

                             uint8_t* WEBP_RESTRICT const yuv_out,

                             int mode) {

  const VP8Encoder* const enc = it->enc;

  const uint8_t* const ref = it->yuv_p + VP8I4ModeOffsets[mode];

  const VP8SegmentInfo* const dqm = &enc->dqm[it->mb->segment];

  int nz = 0;

  int16_t tmp[16];

  VP8FTransform(src, ref, tmp);

  if (DO_TRELLIS_I4 && it->do_trellis) {

    const int x = it->i4 & 3, y = it->i4 >> 2;

    const int ctx = it->top_nz[x] + it->left_nz[y];

    nz = TrellisQuantizeBlock(enc, tmp, levels, ctx, TYPE_I4_AC, &dqm->y1,

                              dqm->lambda_trellis_i4);

  } else {

    nz = VP8EncQuantizeBlock(tmp, levels, &dqm->y1);

  }

  VP8ITransform(ref, tmp, yuv_out, 0);

  return nz;

}

//------------------------------------------------------------------------------

// DC-error diffusion

// Diffusion weights. We under-correct a bit (15/16th of the error is actually

// diffused) to avoid 'rainbow' chessboard pattern of blocks at q~=0.

#define C1 7    // fraction of error sent to the 4x4 block below

#define C2 8    // fraction of error sent to the 4x4 block on the right

#define DSHIFT 4

#define DSCALE 1   // storage descaling, needed to make the error fit int8_t

// Quantize as usual, but also compute and return the quantization error.

// Error is already divided by DSHIFT.

static int QuantizeSingle(int16_t* WEBP_RESTRICT const v,

                          const VP8Matrix* WEBP_RESTRICT const mtx) {

  int V = *v;

  const int sign = (V < 0);

  if (sign) V = -V;

  if (V > (int)mtx->zthresh[0]) {

    const int qV = QUANTDIV(V, mtx->iq[0], mtx->bias[0]) * mtx->q[0];

    const int err = (V - qV);

    *v = sign ? -qV : qV;

    return (sign ? -err : err) >> DSCALE;

  }

  *v = 0;

  return (sign ? -V : V) >> DSCALE;

}

static void CorrectDCValues(const VP8EncIterator* WEBP_RESTRICT const it,

                            const VP8Matrix* WEBP_RESTRICT const mtx,

                            int16_t tmp[][16],

                            VP8ModeScore* WEBP_RESTRICT const rd) {

  //         | top[0] | top[1]

  // --------+--------+---------

  // left[0] | tmp[0]   tmp[1]  <->   err0 err1

  // left[1] | tmp[2]   tmp[3]        err2 err3

  //

  // Final errors {err1,err2,err3} are preserved and later restored

  // as top[]/left[] on the next block.

  int ch;

  for (ch = 0; ch <= 1; ++ch) {

    const int8_t* const top = it->top_derr[it->x][ch];

    const int8_t* const left = it->left_derr[ch];

    int16_t (* const c)[16] = &tmp[ch * 4];

    int err0, err1, err2, err3;

    c[0][0] += (C1 * top[0] + C2 * left[0]) >> (DSHIFT - DSCALE);

    err0 = QuantizeSingle(&c[0][0], mtx);

    c[1][0] += (C1 * top[1] + C2 * err0) >> (DSHIFT - DSCALE);

    err1 = QuantizeSingle(&c[1][0], mtx);

    c[2][0] += (C1 * err0 + C2 * left[1]) >> (DSHIFT - DSCALE);

    err2 = QuantizeSingle(&c[2][0], mtx);

    c[3][0] += (C1 * err1 + C2 * err2) >> (DSHIFT - DSCALE);

    err3 = QuantizeSingle(&c[3][0], mtx);

    // error 'err' is bounded by mtx->q[0] which is 132 at max. Hence

    // err >> DSCALE will fit in an int8_t type if DSCALE>=1.

    assert(abs(err1) <= 127 && abs(err2) <= 127 && abs(err3) <= 127);

    rd->derr[ch][0] = (int8_t)err1;

    rd->derr[ch][1] = (int8_t)err2;

    rd->derr[ch][2] = (int8_t)err3;

  }

}

static void StoreDiffusionErrors(VP8EncIterator* WEBP_RESTRICT const it,

                                 const VP8ModeScore* WEBP_RESTRICT const rd) {

  int ch;

  for (ch = 0; ch <= 1; ++ch) {

    int8_t* const top = it->top_derr[it->x][ch];

    int8_t* const left = it->left_derr[ch];

    left[0] = rd->derr[ch][0];            // restore err1

    left[1] = 3 * rd->derr[ch][2] >> 2;   //     ... 3/4th of err3

    top[0]  = rd->derr[ch][1];            //     ... err2

    top[1]  = rd->derr[ch][2] - left[1];  //     ... 1/4th of err3.

  }

}

#undef C1

#undef C2

#undef DSHIFT

#undef DSCALE